Question: Divide. Write your answer in simplest form. $ \dfrac{1}{7} \div \dfrac{2}{5} = {?} $
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{2}{5}$ is $\dfrac{5}{2}$. Therefore: $ \dfrac{1}{7} \div \dfrac{2}{5} = \dfrac{1}{7} \times \dfrac{5}{2} $ $ \phantom{\dfrac{1}{7} \div \dfrac{2}{5}} = \dfrac{1 \times 5}{7 \times 2} $ $ \phantom{\dfrac{1}{7} \div \dfrac{2}{5}} = \dfrac{5}{14} $